## ON THE CONNECTED DETOUR MONOPHONIC NUMBER OF A GRAPH

## ON THE CONNECTED DETOUR MONOPHONIC NUMBER OF A GRAPH

*P. Titus, K. Ganesamoorthy*

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## Abstract

For a connected graph G = (V;E) of order at least two, a connected detour monophonic set S of G is called a minimal connected detour monophonic set if no proper subset of S is a connected detour monophonic set of G. The upper connected detour monophonic number of G, denoted by dm+c (G), is dened as the maximum cardinality of a minimal connected detour monophonic set of G. We determine bounds for it and nd the same for some special classes of graphs. For any three positive integers a; b and n with 6 a n b, there is a connected graph G with dmc(G) = a, dm+c (G) = b and a minimal connected detour monophonic set of cardinality n.

## Keywords

detour monophonic set, connected detour monophonic set, connected detour monophonic number, minimal connected detour monophonic set, upper connected detour monophonic number.